湍流和转捩过程中拟序结构的识别研究

The identification of coherent structures in turbulence and flow transition has become the most promising tool to reveal the secrets of turbulence and to instruct turbulence modeling. However, as two most popular methods to extract coherent structure from detailed 3-dimensional flow field, both vortex identification methods and reduced order modelling suffer from some problems. For example, because of the lacking of a mathematical definition of vortices and the fact that main vortex identification methods are iso-surface based, it is difficult to analyze the vortex interaction mechanism. In addition, despite the progressive development of reduced order modelling, especially the dynamical mode decomposition (DMD) method, its ability to tackle large-scale data is still limited. Therefore, a systematic method unifying vortex identification method and DMD is developed in this project. Firstly, the interaction mechanism between vortices will be studied based on our proposed Omega vortex identification and a profound understanding of vortex structure. Secondly, an efficient DMD method will be developed targeting to the huge amount of data obtained from direct numerical simulation (DNS). The research work in this project could offer a systematic way to identify coherent structure in turbulent and transitional flows.

拟序结构的精确识别已成为科学上解决湍流问题和工程上湍流建模的关键。在现有的研究中，涡识别方法和动力学系统低维降阶技术是从三维流场中提取拟序结构最主要的两种方法。然而，涡结构本质定义的缺失和主流涡识别方法都基于等值面的事实，使得湍流中涡系结构相互作用机理的研究受到很大限制。此外，尽管以动力学模态分解（DMD）为代表的动力学系统降阶技术得到迅猛发展，但将其应用到直接数值模拟所得到的大规模数据上仍存在困难。因此，本项目建议通过发展和结合涡识别方法和DMD方法，提出识别拟序结构的系统方法。首先，在申请人提出的Omega涡识别方法基础上，进一步加深对涡结构的物理认识，研究涡系结构之间的作用机理。其次，发展DMD方法，解决其应用到大规模数据时存在的问题。通过本项目的研究，可以给出在湍流和转捩流动中识别拟序结构的系统方法，为湍流生成、发展和维持机理研究提供有效的工具。

湍流拟序结构结构与涡结构紧密相连，其精确识别已成为科学上解决湍流问题和工程上湍流建模的关键。本项研究针对涡识别方法和动力学系统低维降技术对拟序结构的识别开展研究，尤其是在涡的定义和识别上，先后参与提出Omega涡识别方法和Rortex涡定义和识别系统。基于Rortex向量能够给出流体运动的局部刚性旋转部分，回答涡的六大要素问题，即涡的绝对强度由Rortex的大小表示，代表当地流体刚体旋转部分角速度的二倍；相对强度由Rortex-Omega方法衡量，代表当地流体的刚性；当地旋转轴即Rortex向量的方向，由速度梯度张量的实特征向量决定；涡核中心即为Rortex涡核线；涡核大小可以按从涡核中心处相对强度减少至涡核处95%这一标准确定；涡边界指流场中涡区和非涡区的边界，可以用Rortex-Omega方法的参数=0.52的等值面来表示。Rortex理论系统及涡识别的六大要素提供了对流场拟序涡结构更精确的刻画，基于此可以帮助我们更好的理解流场，甚至更高效的控制流场。

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